ALBERT

Description:    Suppose that Alice and Bob make local two-outcome measurements on a shared entangled quantum state. We show that, for all positive integers d , there exist correlations that can only be reproduced if the local Hilbert-space dimension is at least d . This establishes that the amount of entanglement required to maximally violate a Bell inequality must depend on the number of measurement settings, not just the number of measurement outcomes. We prove this result by establishing a lower bound on a new generalization of Grothendieck’s constant. Content Type Journal Article Pages 1-17 DOI 10.1007/s00220-011-1280-3 Authors Jop Briët, Centrum Wiskunde & Informatica (CWI), and University of Amsterdam, Science Park 123, 1098 SJ Amsterdam, The Netherlands Harry Buhrman, Centrum Wiskunde & Informatica (CWI), and University of Amsterdam, Science Park 123, 1098 SJ Amsterdam, The Netherlands Ben Toner, School of Physics, The University of Melbourne, Victoria, 3010 Australia Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of \mathbb C . As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed. Content Type Journal Article Pages 1-45 DOI 10.1007/s00220-011-1286-x Authors Semyon Dyatlov, Department of Mathematics, Evans Hall, University of California, Berkeley, CA 94720, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Erratum to: A KAM Theorem with Applications to Partial Differential Equations of Higher Dimensions Content Type Journal Article Pages 1-1 DOI 10.1007/s00220-011-1283-0 Authors Xiaoping Yuan, School of Mathematical Sciences, Fudan University, Shanghai, 200433 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain information-theoretic operational interpretations, e.g., the min-entropy as maximum achievable quantum correlation, and the max-entropy as decoupling accuracy. We furthermore generalize the smoothed versions of these entropies and prove an infinite-dimensional quantum asymptotic equipartition property. To facilitate these generalizations we show that the min- and max-entropy can be expressed in terms of convergent sequences of finite-dimensional min- and max-entropies, which provides a convenient technique to extend proofs from the finite to the infinite-dimensional setting. Content Type Journal Article Pages 1-22 DOI 10.1007/s00220-011-1282-1 Authors Fabian Furrer, Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover, Germany Johan Åberg, Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Renato Renner, Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition of admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-011-1292-z Authors Xi Zhang, Department of Mathematics, Zhejiang University, Hangzhou, 310027 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density ρ ph including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no ‘real’ electron. We show that ρ ph admits an asymptotic expansion to any order in powers of the physical coupling constant α ph , provided that the ultraviolet cut-off behaves as L ~ e 3 p (1 - Z 3 )/2 a ph 〉〉 1 . The renormalization parameter 0 〈  Z 3  〈 1 is defined by Z 3  =  α ph / α , where α is the bare coupling constant. The coefficients of the expansion of ρ ph are independent of Z 3 , as expected. The first order term gives rise to the well-known Uehling potential, whereas the higher order terms satisfy an explicit recursion relation. Content Type Journal Article Pages 1-33 DOI 10.1007/s00220-011-1271-4 Authors Philippe Gravejat, Centre de Mathématiques Laurent Schwartz (UMR 7640), École Polytechnique, 91128 Palaiseau Cedex, France Mathieu Lewin, CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, 95000 Cergy-Pontoise, France Éric Séré, Ceremade (UMR 7534), Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (in J. Phys. (USSR) IX:25–40, 1945 ), Kirzhnits and Nepomnyashchii (in Sov. Phys. JETP 32:1191–1197, 1971 ), and Likos et al . (in J. Chem. Phys. 126:224502, 2007 ). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superimposed on the sites of a close-packed lattice. Content Type Journal Article Pages 1-54 DOI 10.1007/s00220-011-1276-z Authors András Sütő, Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P. O. B. 49, 1525 Budapest, Hungary Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G . For any simple G , there exist compact manifolds with the same classical equivariant cohomology, which can be distinguished by this invariant. When M is a point, this cohomology is an interesting conformal vertex algebra whose structure is still mysterious. In this paper, we scratch the surface of this object in the case G  =  SU (2). Content Type Journal Article Pages 1-37 DOI 10.1007/s00220-011-1284-z Authors Andrew R. Linshaw, Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This paper is devoted to the study of strong or weak solutions of the Navier–Stokes equations in the case of an homogeneous initial data. The case of small initial data is discussed. For large initial data, an approximation is developed, in the spirit of a paper of Vishik and Fursikov. Qualitative convergence is obtained by use of the theory of Muckenhoupt weights. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-011-1291-0 Authors Pierre Gilles Lemarié–Rieusset, Équipe Analyse et Probabilités, EA2172, Université d’Evry Val d’Essonne, 91025 Evry cedex, France Frédéric Lelièvre, Équipe Analyse et Probabilités, EA2172, Université d’Evry Val d’Essonne, 91025 Evry cedex, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: In the future, climate models predict an increase in global surface temperature and during winter a changing of precipitation from less snowfall to more raining. Without protective snow cover, freezing can be more intensive and can enter noticeably deeper into the soil with effects on C cycling and soil organic matter (SOM) dynamics. We removed the natural snow cover in a Norway spruce forest in the Fichtelgebirge Mts. during winter from late December 2005 until middle of February 2006 on three replicate plots. Hence, we induced soil frost to 15 cm depth (at a depth of 5 cm below surface up to –5°C) from January to April 2006, while the snow-covered control plots never reached temperatures 〈 0°C. Quantity and quality of SOM was followed by total organic C and biomarker analysis. While soil frost did not influence total organic-C and lignin concentrations, the decomposition of vanillyl monomers (Ac/Ad) V and the microbial-sugar concentrations decreased at the end of the frost period, these results confirm reduced SOM mineralization under frost. Soil microbial biomass was not affected by the frost event or recovered more quickly than the accumulation of microbial residues such as microbial sugars directly after the experiment. However, in the subsequent autumn, soil microbial biomass was significantly higher at the snow-removal (SR) treatments compared to the control despite lower CO 2 respiration. In addition, the water-stress indicator (PLFA [cy17:0 + cy19:0] / [16:1ω7c + 18:1ω7c]) increased. These results suggest that soil microbial respiration and therefore the activity was not closely related to soil microbial biomass but more strongly controlled by substrate availability and quality. The PLFA pattern indicates that fungi are more susceptible to soil frost than bacteria.

Description:    We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure. Content Type Journal Article Pages 1-15 DOI 10.1007/s00220-011-1275-0 Authors F. Rodriguez Hertz, IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay M. A. Rodriguez Hertz, IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay A. Tahzibi, Departamento de Matemática, ICMC-USP São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil R. Ures, IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study non-associative twisted group algebras over (\mathbb Z 2 ) n with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion. We present two applications of the constructed algebras and the developed technique. The first application is a simple explicit formula for the following famous square identity: ( a 1 2 + ¼ + a N 2 ) ( b 1 2 + ¼ + b r ( N ) 2 ) = c 1 2 + ¼ + c N 2 , where c k are bilinear functions of the a i and b j and where ρ ( N ) is the Hurwitz-Radon function. The second application is the relation to Moufang loops and, in particular, to the code loops. To illustrate this relation, we provide an explicit coordinate formula for the factor set of the Parker loop. Content Type Journal Article Pages 1-36 DOI 10.1007/s00220-011-1279-9 Authors Sophie Morier-Genoud, Institut Mathématiques de Jussieu, UMR 7586, Université Pierre et Marie Curie Paris VI, 4 Place Jussieu, Case 247, 75252 Paris Cedex 05, France Valentin Ovsienko, CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    For n ≥ 7, we give the optimal estimate for the second eigenvalue of Paneitz operators for compact n -dimensional submanifolds in an ( n  +  p )-dimensional space form in terms of the mean curvature and the Q-curvature. Content Type Journal Article Pages 1-8 DOI 10.1007/s00220-011-1281-2 Authors Daguang Chen, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 P.R. China Haizhong Li, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve. Content Type Journal Article Pages 1-16 DOI 10.1007/s00220-011-1274-1 Authors José Aliste-Prieto, Centro de Modelamiento Matemático, Universidad de Chile, Blanco Encalada 2120 7to. piso, Santiago, Chile Daniel Coronel, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Campus San Joaquín, Avenida Vicuña Mackenna 4860, Santiago, Chile Jean-Marc Gambaudo, Laboratoire J.-A. Dieudonné, Université de Nice - Sophia Antipolis, CNRS, 06108 Nice Cedex 02, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [−1, 1]. It is shown that the correlation kernels in the bulk are given by the incomplete Beta kernel, as expected. As a consequence it is established that the local correlation functions in the scaling limit do not depend on the particular sequence of discrete inner shapes that converge to V . A detailed analysis of the correlation kernels at the top of the limit shape, and of the frozen boundary is given. It is shown that depending on the slope of the linear section of the back wall, the system exhibits behavior observed in either Okounkov and Reshetikhin (Commun Math Phys 269(3):571–609, 2007 ) or Boutillier et al. ( http://arXiv.org/abs/0912.3968v2 [math-ph], 2009 ). Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-011-1277-y Authors Sevak Mkrtchyan, Department of Mathematics, Rice University, Houston, TX 77005, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling. Content Type Journal Article Pages 1-36 DOI 10.1007/s00220-011-1278-x Authors J. Faupin, Institut de Mathématiques de Bordeaux, UMR-CNRS 5251, Université de Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France J. S. Møller, Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, 8000 Aarhus C, Denmark E. Skibsted, Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, 8000 Aarhus C, Denmark Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Knuth’s parking scheme is a model in computer science for hashing with linear probing. One may imagine a circular parking lot with n sites; cars arrive at each site with unit rate. When a car arrives at a vacant site, it parks there; otherwise it turns clockwise and parks at the first vacant site which is found. We incorporate fires into this model by throwing Molotov cocktails on each site at a smaller rate n − α , where 0 〈  α  〈 1 is a fixed parameter. When a car is hit by a Molotov cocktail, it burns and the fire propagates to the entire occupied interval which turns vacant. We show that with high probability when n → ∞, the parking lot becomes saturated at a time close to 1 (i.e. as in the absence of fire) for α  〉 2/3, whereas for α  〈 2/3, the average occupation approaches 1 at time 1 but then quickly drops to 0 before the parking lot is ever saturated. Our study relies on asymptotics for the occupation of the parking lot without fires in certain regimes which may be of independent interest. Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-011-1288-8 Authors Jean Bertoin, Laboratoire de Probabilités et Modèles Aléatoires, UPMC, Case courrier 188, 4 Place Jussieu, 75252 Paris, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit. Content Type Journal Article Pages 1-14 DOI 10.1007/s00220-011-1261-6 Authors Robert Seiringer, Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider the perturbed mKdV equation ¶ t u = - ¶ x ( ¶ x 2 u + 2 u 3 - b ( x , t ) u ) , where the potential b ( x , t )= b 0 ( hx , ht ), 0 〈 h 〈〈 1 , is slowly varying with a double soliton initial data. On a dynamically interesting time scale the solution is O ( h 2 ) close in H 2 to a double soliton whose position and scale parameters follow an effective dynamics, a simple system of ordinary differential equations. These equations are formally obtained as Hamilton’s equations for the restriction of the mKdV Hamiltonian to the submanifold of solitons. The interplay between algebraic aspects of complete integrability of the unperturbed equation and the analytic ideas related to soliton stability is central in the proof. Content Type Journal Article Pages 1-63 DOI 10.1007/s00220-011-1252-7 Authors Justin Holmer, Department of Mathematics, Brown University, 151 Thayer Street, Providence, RI 02912, USA Galina Perelman, Ecole Polytechnique, CMLS, 91128 Palaiseou, France Maciej Zworski, Department of Mathematics, University of California, Berkeley, CA 94720, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The partition function of N =6 supersymmetric Chern–Simons-matter theory (known as ABJM theory) on \mathbb S 3 , as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS 4 ×\mathbb C \mathbb P 3 and gives the correct N 3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in \mathbb C \mathbb P 3 . We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus. Content Type Journal Article Pages 1-53 DOI 10.1007/s00220-011-1253-6 Authors Nadav Drukker, Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany Marcos Mariño, Département de Physique Théorique, Université de Genève, Genève, CH-1211 Switzerland Pavel Putrov, Section de Mathématiques, Université de Genève, Genève, CH-1211 Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove unique continuation properties for solutions of the evolution Schrödinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions and the possible profiles of the traveling waves solutions of semi-linear Schrödinger equations. Content Type Journal Article Pages 1-26 DOI 10.1007/s00220-011-1256-3 Authors L. Escauriaza, Dpto. de Matemáticas, UPV/EHU, Apto. 644, 48080 Bilbao, Spain C. E. Kenig, Department of Mathematics, University of Chicago, Chicago, IL 60637, USA G. Ponce, Department of Mathematics, University of California, Santa Barbara, CA 93106, USA L. Vega, Dpto. de Matemáticas, UPV/EHU, Apto. 644, 48080 Bilbao, Spain Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this article we consider the physical justification of the Vortex-Wave equation introduced by Marchioro and Pulvirenti (Mechanics, analysis and geometry: 200 years after Lagrange, North-Holland Delta Ser., Amsterdam, North-Holland, pp. 79–95, 1991 ), in the case of a single point vortex moving in an ambient vorticity. We consider a sequence of solutions for the Euler equation in the plane corresponding to initial data consisting of an ambient vorticity in L 1 ∩ L ∞ and a sequence of concentrated blobs which approach the Dirac distribution. We introduce a notion of a weak solution of the Vortex-Wave equation in terms of velocity (or primitive variables) and then show, for a subsequence of the blobs, the solutions of the Euler equation converge in velocity to a weak solution of the Vortex-Wave equation. Content Type Journal Article Pages 1-21 DOI 10.1007/s00220-011-1215-z Authors Clayton Bjorland, Department of Mathematics, University of Texas, Austin, TX 78712-0257, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-011-1210-4 Authors Claudio Dappiaggi, II. Institut für Theoretische Physik, D-22763 Hamburg, Deutschland Gandalf Lechner, Faculty of Physics, University of Vienna, A-1090 Vienna, Austria Eric Morfa-Morales, Erwin Schrödinger Institute for Mathematical Physics, Vienna, A-1090 Vienna, Austria Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellians. The Maxwellians are constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations. Content Type Journal Article Pages 1-52 DOI 10.1007/s00220-011-1207-z Authors Jared Speck, Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB United Kingdom Robert M. Strain, Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Intensive land use may affect soil properties ( e.g., decreased soil organic matter [SOM] content) and, consequently, reduce crop yields considerably. One way of counteracting the loss of SOM and stimulating plant productivity could be the use of organic residues from agro-industrial processes as bioactive products. The present study was focused on the possible effects of phenol-containing organic substances derived from agro-industrial by-products on maize ( Zea mays L.) metabolism in a pot experiment. Plants were grown for 12 d in a nutrient solution in the absence (control) or in the presence of either a cellulosolitic dry apple hydrolyzate (AP) or a dry blueberry cool extract (BB) applied at two rates (0.1 and 1 mL L –1 ). Both products increased root and leaf biomass and led to higher concentrations of macronutrients in the plant tissue. AP and BB also had a positive impact on nitrogen (N) metabolism stimulating the activity and gene expression of phenylalanine ammonia-lyase, a key enzyme of the phenylpropanoid pathway. Furthermore, both products increased leaf concentrations of phenols (+ 28% and 49% for AP and BB, respectively) and flavonoids (+ 22% and 25% for AP and BB, respectively). From our results it can be assumed that residues from agro-industry may be successfully used as bioactive products in agriculture to increase plant yield and resistance to stress conditions.

Description:    For an infinitely renormalizable quadratic map f c : z ® z 2 + c with the sequence of renormalization periods { k m } and rotation numbers { t m  =  p m / q m }, we prove that if $${\limsup k_m^{-1} \log |p_m| 〉0 }$$, then the Mandelbrot set is locally connected at c . We prove also that if limsup | t m +1 | 1/ q m 〈 1 and q m → ∞, then the Julia set of f c is not locally connected and the Mandelbrot set is locally connected at c provided that all the renormalizations are non-primitive (satellite). This quantifies a construction of A. Douady and J. Hubbard, and weakens a condition proposed by J. Milnor. Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-011-1228-7 Authors Genadi Levin, Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904 Israel Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: An agricultural use of reclaimed coal-mine spoil banks is limited to nonfood crop uses and provides potential for biofuel crops. Two high-biomass crops— Galega orientalis and Helianthus tuberosus —were cultivated in a greenhouse pot experiment conducted in sterilized and nonsterile spoil bank clay. We aimed (1) to determine the possibility of reducing the applied rate of organic amendments (thus decreasing the costs of spoil-bank reclamation) and (2) to assess whether the inoculation with arbuscular mycorrhizal fungi (AMF) can improve plant growth and biomass accumulation of bioenergy crops even in nonsterile soil containing naturally occurring AMF. The spoil substrate was either unamended or treated with a mixture of composted urban waste and ligno-cellulose at a rate corresponding to 40 t ha –1 . Three native AMF isolates or three isolates from the International Bank of Glomeromycota (BEG) originating from man-made ecosystems were used for inoculation. Generally, both plant species positively responded to both mycorrhizal inoculation and organic amendment. While G. orientalis did not show any preferences towards the AMF inoculum origin in the nonsterile soil, for H. tuberosus the specific combination of organic amendment and BEG isolates resulted in highest yields of shoot biomass. The study shows that the successful planting of both tested crops requires the organic amendment. However, its dosage can be substantially reduced. The effectiveness of mycorrhizal inoculation can vary for the combination of plant species and the origin of the applied AMF.

Description: Iodine is an essential element in the human diet, and iodine deficiency is a significant health problem. No attempts to increase iodine content in plant-derived food (biofortification) have so far been particularly effective. We studied iodine uptake in tomato ( Solanum lycopersicum L.) to evaluate whether it is possible to increase the iodine concentration in its fruits. Iodine translocation and storage inside tomato tissues were studied using radioactive iodine. Potassium iodide was also supplied at different concentrations to tomato plants to evaluate the resulting iodide concentration both in the vegetative tissues and the fruits. The results indicate that iodine was taken up better when supplied to the roots using hydroponically grown plants. However, a considerable amount of iodine was also stored after leaf treatment, suggesting that iodine transport through phloem also occurred. We found that tomato plants can tolerate high levels of iodine, stored both in the vegetative tissues and fruits at concentrations that are more than sufficient for the human diet. We conclude that tomato is an excellent crop for iodine-biofortification programs.

Description:    Oseledets regularity functions quantify the deviation of the growth associated with a dynamical system along its Lyapunov bundles from the corresponding uniform exponential growth. The precise degree of regularity of these functions is unknown. We show that for every invariant Lyapunov bundle of a volume preserving Anosov flow on a closed smooth Riemannian manifold, the corresponding Oseledets regularity functions are in L p ( m ), for some p 〉 0, where m is the probability measure defined by the volume form. We prove an analogous result for essentially bounded cocycles over volume preserving Anosov flows. Content Type Journal Article Pages 1-21 DOI 10.1007/s00220-011-1255-4 Authors Slobodan N. Simić, Department of Mathematics, San José State University, San José, CA 95192-0103, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Citrus established in calcareous soils can be affected by iron (Fe)-deficiency chlorosis which limits yield and the farmers' income. The degree of deficiency depends on the rootstock, but the resistance to Fe chlorosis still requires further investigation. To study physiological parameters of citrus rootstocks that could be used to evaluate resistance to Fe deficiency, plants of Troyer citrange ( Citrus sinensis L. Osb. × Poncitrus trifoliata L. Raf.), Carrizo citrange, Volkamer lemon ( Citrus volkameriana Ten. & Pasq.), alemow ( Citrus macrophylla Wester), and sour orange ( Citrus aurantium L.) were grown in nutrient solutions with 0, 5, 10, 15, or 20 μM Fe. For each rootstock, plant height, root and shoot dry weights, and concentration of Fe in the shoots and roots were measured at the end of the experiment. Chlorophyll (CHL) concentration was estimated throughout the experimental period using a portable CHL meter (SPAD-502) calibrated for each rootstock. At the end of the experiment, CHL fluorescence parameters were measured in each rootstock with a portable fluorimeter. Maximal and variable fluorescence values indicated that the photochemistry of Troyer was more affected by a low concentration of Fe in the nutrient solution than that of other rootstocks. To compare rootstocks, the absolute CHL concentration was converted into relative yield by employing a scaling divisor based on the maximum value of total CHL in plants without Fe-deficiency symptoms. Exponential models were developed to determine the minimum Fe concentration in nutrient solution required to maintain leaf CHL at 50% of the maximum CHL concentration (IC50). Models were also developed to assess the period of time the rootstocks were able to grow under Fe-stress conditions before they reached IC50. Volkamer lemon and sour orange needed the lowest Fe concentration (between 4 and 5 μM Fe) to maintain IC50, and Troyer citrange had the highest Fe requirement (14 μM Fe). Citrus macrophylla and Carrizo citrange required 7 and 9 μM of Fe, respectively. Similarly, Volkamer lemon and sour orange rootstocks withstood more days under total Fe depletion or with a low concentration of Fe (5 μM Fe in nutrient solution) until they reached IC50, compared to the other rootstocks. The approach used led to a classification of the rootstocks into three categories, regarding their internal tolerance to Fe chlorosis: resistance (sour orange and Volkamer lemon), intermediate resistance (C . macrophylla and Carrizo citrange), and reduced resistance (Troyer citrange).

Description: Trees interact in a complex manner with soils: they recycle and redistribute nutrients via many ecological pathways. Nutrient distribution via leaf litter is assumed to be of major importance. Beech is commonly known to have lower nutrient concentrations in its litter than other hardwood tree species occurring in Central Europe. We examined the influences of distribution of beech ( Fagus sylvatica L.), ash ( Fraxinus excelsior L.), lime ( Tilia cordata Mill. and T. platyphyllos Scop.), maple ( Acer spp. L.), and clay content on small-scale variability of pH and exchangeable Ca and Mg stocks in the mineral soil and of organic-C stocks in the forest floor in a near-natural, mature mixed deciduous forest in Central Germany. The soil is a Luvisol developed in loess over limestone. We found a positive effect of the proportion of beech on the organic-C stocks in the forest floor and a negative effect on soil pH and exchangeable Ca and Mg in the upper mineral soil (0 to 10 cm). The proportion of ash had a similar effect in the opposite direction, the other species did not show any such effect. The ecological impact of beech and ash on soil properties at a sample point was explained best by their respective proportion within a radius of 9 to 11 m. The proportion of the species based on tree volume within this radius was the best proxy to explain species effects. The clay content had a significant positive influence on soil pH and exchangeable Ca and Mg with similar effect sizes. Our results indicate that beech, in comparison to other co-occurring deciduous tree species, mainly ash, increased acidification at our site. This effect occurred on a small spatial scale and was probably driven by species-related differences in nutrient cycling via leaf litter. The distribution of beech and ash resulted not only in aboveground diversity of stand structures but also induced a distinct belowground diversity of the soil habitat.

Description: Several chemical and microbial properties of mine soils need to be measured for comprehensive assessment of the reclamation success. The objective of this study was to evaluate the ability of NIR spectroscopy to predict organic C (C org ), total N (N t ), and several microbial properties of mine soils reclaimed for forestry. Soils samples ( n = 154) were collected at two reclaimed areas in central and S Poland, and their spectra in the NIR region (including the visible range, 400–2500 nm) were recorded. A half of the samples was used to develop calibration equations, and another half was used for validation. The modified partial least squares regression was applied to build calibration equations using the whole spectrum (0 to 2nd derivative). The best predictions were obtained for C org and N t (ratio of standard deviation to standard error of prediction in the validation stage [RPD] = 3.4 and 4.1; the regressions coefficients [ a ] of linear regression [measured against predicted values] = 0.94 and 0.96; correlation coefficients [ r ] = 0.96 and 0.97, respectively). Very well predictive models applicable for quantitative measurements were obtained also for microbial biomass, basal respiration, and the activities of dehydrogenase and acid phosphatase (RPD = 2.3–2.5, a = 0.90–0.99, r = 0.90–0.92). Prediction of urease activity was slightly worse (RPD = 2.1, a = 0.88, r = 0.87) but sufficient for rough estimation. The obtained results indicated the ability of NIR spectroscopy to predict complex soil microbial properties. Therefore, application of this analytical method may improve the assessment of recovery of microbial functions in reclaimed post-mining barrens.

Description: Several algorithms exist for the calibration procedures of near-infrared spectra in soil-scientific studies, but the potential of a genetic algorithm (GA) for spectral feature selection and interpretation has not yet been sufficiently explored. Objectives were (1) to test the usefulness of near-infrared spectroscopy (NIRS) for a prediction of C and N from char and forest-floor Oa material in soils using either a partial least squares (PLS) method or a GA-PLS approach and (2) to discuss the mechanisms of GA feature selection for the examined constituents. Calibration and validation were carried out for measured reflectance spectra in the visible and near-IR region (400–2500 nm) on an existing set of 432 artificial mixtures of C-free soil, char (lignite, anthracite, charcoal, or a mixture of the three coals), and forest-floor Oa material. For all constituents (total C and N, C and N from all coals and from the Oa material, C derived from mixed coal, charcoal, lignite, and anthracite), the GA-PLS approach was superior over the full-spectrum PLS method. The RPD values (ratio of standard deviation of the laboratory results to standard error of prediction) ranged from 2.4 to 5.1 in the validation and indicated a better category of prediction for three constituents: “approximate quantitative” instead of a “distinction between high and low” for C derived from mixed coal and “good” instead of “approximate quantitative” for C and N derived from all coals. Overall, this study indicates that the approach using GA may have a greater potential than the PLS method in NIRS.

Description: Several genes in the aspen genome have been modified to generate stem wood with lower lignin content and an altered lignin composition. Lower lignin in wood reduces the time and energy required for pulping. Further, this modification can also increase the allocation of photosynthate to cellulose and total biomass production, potentially increasing CO 2 -sequestration capacity. However, widespread planting of trees with altered lignin content and composition could alter soil organic-C dynamics in complex ways. To further examine the effects of altered lignin biosynthesis on plant growth and accrual of soil organic C (SOC), we conducted a repeated greenhouse study with four lines of transgenic aspen ( Populus tremuloides Michx.) and one wild-type (control) aspen. Accrual of aspen-derived SOC was quantified by growing aspen trees (C3 plants) in C4 soil and measuring changes in the natural abundance of δ 13 C. We measured plant growth, biomass, and C content and combined these data with SOC measurements to create C budgets for the plant mesocosms. Lignin modifications resulted in differences in the accrual of aspen-derived SOC and total mesocosm C, primarily due to differences in biomass between genetically modified lines of aspen. One genetic alteration (low lignin, line 23) was able to perform similarly or better than the wild-type aspen (control, line 271) without altering SOC. Alterations in lignin structure (S : G ratios) had negative effects on biomass production and SOC formation. The addition of new (aspen-derived) SOC was proportional to the loss of existing SOC, evidence for a priming effect. The pool of new SOC was related to total plant biomass, suggesting that the effects of lignin modification on SOC are driven by changes in plant growth.

Description:    The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel’s entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels. Content Type Journal Article Pages 1-37 DOI 10.1007/s00220-011-1309-7 Authors Mario Berta, Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Matthias Christandl, Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Renato Renner, Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action is sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies. We show this by explicitly computing the nonperturbative spectral action for some candidate flat cosmic topologies given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the flat torus by a multiplicative factor, similarly to what happens in the case of the spectral action of the spherical forms in relation to the case of the 3-sphere. We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case. Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-011-1352-4 Authors Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA Elena Pierpaoli, Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA Kevin Teh, Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove the limiting absorption principle for a dressed electron at a fixed total momentum in the standard model of non-relativistic quantum electrodynamics. Our proof is based on an application of the smooth Feshbach-Schur map in conjunction with Mourre’s theory. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-011-1339-1 Authors T. Chen, Department of Mathematics, University of Texas at Austin, Austin, TX, USA J. Faupin, Institut de Mathématiques de Bordeaux, UMR-CNRS 5251, Université de Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France J. Fröhlich, Institut für Theoretische Physik, ETH Hönggerberg, 8093 Zürich, Switzerland I. M. Sigal, Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of Franz (The Theory of Quantum Levy Processes, http://arxiv.org/abs/math/0407488v1 [math.PR], 2009 ), Schürmann (White noise on bioalgebras. Volume 1544 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1993 ) and others, and then formulate and study in details (with a number of interesting examples) a definition of quantum Brownian motions on those non-commutative manifolds (a la Connes) which are quantum homogeneous spaces of their quantum isometry groups in the sense of Goswami (Commun Math Phys 285(1):141–160, 2009 ). We prove that bi-invariant quantum Brownian motion can be ‘deformed’ in a suitable sense. Moreover, we propose a non-commutative analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics for a specific example on non-commutative two-torus A q , which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that A q is a non-commutative model of the (locally one-dimensional) ‘leaf-space’ of the Kronecker foliation. Content Type Journal Article Pages 1-36 DOI 10.1007/s00220-011-1368-9 Authors Biswarup Das, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108 India Debashish Goswami, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108 India Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Wild barley ( Hordeum sp. ) germplasm is rich in genetic diversity and provides a treasure trove of useful genes for crop improvement. We carried out a comprehensive program combining short-term hydroponic screening via hematoxylin-staining of root-regrowth procedure and filter paper–based evaluation of diverse germplasm in response to Al/acid stress using 105 annual Tibetan wild barley and 45 cultivated barley genotypes. Root elongation among the 105 Tibetan wild barley genotypes varied significantly after Al exposure, ranging from 62.9% to 80.0% in variation coefficients and 4.35 to 4.45 in diversity index. These genotypic differences in Al resistance were fairly consistent in both the hydroponic and filter paper–based evaluations: XZ16, XZ166, and XZ113 were selected as Al-resistant genotypes, and XZ61, XZ45, and XZ98 as Al-sensitive wild genotypes. Furthermore, significantly lower Al concentrations in roots and shoots were detected in the three selected Al-resistant genotypes than in the three sensitive genotypes in the filter paper–based experiment. Meanwhile, XZ16 was the least affected by Al toxicity in regard to reduced SPAD value (chlorophyll meter readings), plant height, root length, dry biomass, tillers per plant, and chlorophyll fluorescence (Fv/Fm) in the long-term hydroponic experiment compared with the Al-resistant cultivated barley cv. Dayton, while XZ61 had the severest stress symptoms.

Description: Simplified algebraic equations are derived to calculate directly the Brooks and Corey model parameters using data obtained from one-step outflow experiments and saturated hydraulic conductivity. The suggested method has been demonstrated only for horticultural substrates and is verified experimentally for four substrates with satisfactory agreement of the results.

Description: Fine roots from the soil archive of the Swedish National Forest Soil Inventory, collected in 1964, 1972, 1985, and 1998, were analyzed for 14 C contents. Two different methods of estimating residence time were compared. Residence time of root C was estimated to be 8 y using a steady state 1-pool model.

Description: Appropriate management of P from slurry can increase crop production and decrease nutrient loss to water bodies. The present study examined how the application of different size fractions of dairy slurry influenced the quantity and composition of P leached from grassland in a temperate climate. Soil blocks were amended (day 0 = start of the experiment) with either whole slurry (WS), the 〉 425 μm fraction (coarse slurry fraction, CSF), the 〈 45 μm slurry fraction (fine liquid slurry fraction, FLF), or not amended, i.e., the control soil (CON). Deionized water was added to the soil blocks to simulate six sequential rainfall events, equivalent to 250 mm (day 0.2, 1.2, 4.2, 11.2) or 500 mm of rainfall (day 18.2 and 25.2), with leachates collected the following day. The results showed that total dissolved P (TDP), dissolved reactive P (DRP), dissolved unreactive P (DUP), orthophosphate, phosphomonoester, and pyrophosphate concentrations generally decreased with the increasing number of simulated rain events. Total dissolved P was leached in the following order WS 〉 FLF ≈ CSF 〉 CON. Dissolved organic C was correlated with TDP, DRP, and DUP in leachates of all treatments. The highest concentrations of dissolved phosphomonoesters and pyrophosphate (147 μg P L –1 and 57 μg P L –1 , respectively) were detected using solution 31 P-NMR spectroscopy in the WS leachates. Overall, there were significant differences observed between slurry treatments ( e.g., relative contributions of inorganic P vs. organic P of dissolved P in leachates). Differences were independent from the rate at which slurry P was applied, because the highest dissolved P losses per unit of slurry P applied were measured in the FLF, i.e., the treatment that received the smallest amount of P. We conclude that the specific particle-size composition of applied slurry influences dissolved P losses from grassland systems. This information should be taken in account in farm-management approaches which aim to minimizing dissolved slurry P losses from grassland systems.

Description:    We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the Källén-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical structure emerges. We apply our results to study the decay of unstable Anti-de Sitter particles. The total amplitude is in this case finite and Anti-de Sitter invariant. Content Type Journal Article Pages 1-37 DOI 10.1007/s00220-011-1372-0 Authors Jacques Bros, Institut de Physique Théorique, CEA, Saclay, France Henri Epstein, Institut des Hautes Études Scientifiques, 91440 Bures-sur-Yvette, France Michel Gaudin, Institut de Physique Théorique, CEA, Saclay, France Ugo Moschella, Università dell’Insubria, 22100 Como, Italy Vincent Pasquier, Institut de Physique Théorique, CEA, Saclay, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i.e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum. Content Type Journal Article Pages 1-36 DOI 10.1007/s00220-011-1373-z Authors László Erdős, Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany David Hasler, Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat Kähler metrics asymptotic to the product of a real line with a flat 3-manifold. Content Type Journal Article Pages 773-794 DOI 10.1007/s00220-011-1366-y Authors Olivier Biquard, Inst. de Math. de Jussieu, case 247, UPMC Université Paris 6, UMR 7586, 4, place Jussieu, 75005 Paris, France Vincent Minerbe, Inst. de Math. de Jussieu, case 247, UPMC Université Paris 6, UMR 7586, 4, place Jussieu, 75005 Paris, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616 Journal Volume Volume 308 Journal Issue Volume 308, Number 3

Description:    We consider the large N limit of the Nahm transform, which relates charge N monopoles to solutions to the Nahm equation involving N × N matrices. In the large N limit the former approaches a magnetic bag, and the latter approaches a solution of the Nahm equation based on the Lie algebra of area-preserving vector fields on the 2-sphere. We show that the Nahm transform simplifies drastically in this limit. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-011-1378-7 Authors Derek Harland, Department of Mathematical Sciences, Durham University, Durham, DH1 3LE UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The formation and propagation of singularities for the Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. In this paper, we consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, and then it propagates only along the forward characteristics inside the domain before it hits on the boundary again. Content Type Journal Article Pages 641-701 DOI 10.1007/s00220-011-1355-1 Authors Chanwoo Kim, Department of Mathematics, Brown University, Providence, RI 02917, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616 Journal Volume Volume 308 Journal Issue Volume 308, Number 3

Description:    We study the massless field on D n = D Ç \tfrac1 n Z 2 , where D Í R 2 is a bounded domain with smooth boundary, with Hamiltonian H ( h ) = å x ~ y   V ( h ( x ) - h ( y )) . The interaction V is assumed to be symmetric and uniformly convex. This is a general model for a (2 + 1)-dimensional effective interface where h represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: h ( x ) = n x · u + f ( x ) for x Î ¶ D n ,  u Î R 2 , and f : R 2 → R continuous. We prove that the fluctuations of linear functionals of h ( x ) about the tilt converge in the limit to a Gaussian free field on D , the standard Gaussian with respect to the weighted Dirichlet inner product ( f , g ) Ñ b = ó õ D   å i   b i ¶ i f i ¶ i g i for some explicit β = β ( u ). In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of h are asymptotically described by SLE (4), a conformally invariant random curve. Content Type Journal Article Pages 591-639 DOI 10.1007/s00220-011-1315-9 Authors Jason Miller, Department of Mathematics, Stanford University, Stanford, CA 94305, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616 Journal Volume Volume 308 Journal Issue Volume 308, Number 3

Description: Erratum to: Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles Content Type Journal Article Category Erratum Pages 1-2 DOI 10.1007/s00220-011-1332-8 Authors C. Carmeli, Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy G. Cassinelli, Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy A. Toigo, Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy V. S. Varadarajan, Department of Mathematics, University of California at Los Angeles, Box 951555, Los Angeles, CA 90095-1555, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Several methods are used for the extraction of soil solution. The objective of this study was to find out to what extent the different extraction methods yield complementary or equivalent information. Soil solutions were sampled once at 10 different forest sites in Germany, with 4 sampling points per site, using 5 different extraction methods. Concentrations of the major ions in the 1:2 extracts and the equilibrium soil-pore solutions (obtained from percolation of field-fresh soil cores) were generally lower than in desorption solutions, suction-cup solutions, and saturation extracts. Surprisingly, the latter three methods generally yielded equivalent results. However, possible systematic differences between these methods could have been masked by the high small-scale spatial variability within the sites.

Description:    We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary. Content Type Journal Article Pages 1-35 DOI 10.1007/s00220-011-1356-0 Authors Philippe Di Francesco, Institut de Physique Théorique du Commissariat à l’Energie Atomique, Unité de Recherche Associée du CNRS, CEA Saclay/IPhT/Bat 774, 91191 Gif sur Yvette Cedex, France Nicolai Reshetikhin, Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-3840, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Erratum to: Fluctuations of the Nodal Length of Random Spherical Harmonics Content Type Journal Article Category Erratum Pages 1-2 DOI 10.1007/s00220-011-1367-x Authors Igor Wigman, Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H ( s ), with finite range interactions depending continuously on s Î [0,1] , such that for each s , H ( s ) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H (0) and H (1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that ’belong to the same phase’ are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an s -dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings’ ‘quasi-adiabatic evolution’ technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the spectral flow , connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models H ( s ), 0 ≤ s  ≤ 1. Content Type Journal Article Pages 1-37 DOI 10.1007/s00220-011-1380-0 Authors Sven Bachmann, Department of Mathematics, University of California, Davis, Davis, CA 95616, USA Spyridon Michalakis, Institute for Quantum Information, California Institute of Technology, Pasadena, CA 91125, USA Bruno Nachtergaele, Department of Mathematics, University of California, Davis, Davis, CA 95616, USA Robert Sims, Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schrödinger equation. In this part we study the diffraction managed discrete non-linear Schrödinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing average diffraction, any solution f Î l 2 (\mathbb Z ) of the non-linear and non-local diffraction management equation decays super-exponentially. More precisely, we have the bound limsup | x | ® ¥   æ è ( | x | +1)ln( | x | +1) ö ø - 1    ln | f ( x ) | £ - \frac14 for any diffraction management soliton. Content Type Journal Article Pages 1-21 DOI 10.1007/s00220-011-1354-2 Authors Dirk Hundertmark, Institute for Analysis, Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany Young-Ran Lee, Department of Mathematics, Sogang University, Shinsu-dong 1, Mapo-gu, Seoul, 121-742 South Korea Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We give a representation-theoretic proof of a conjecture from Rietsch (Adv Math 217:2401–2442, 2008 ) providing integral formulas for solutions to the quantum Toda lattice in general type. This result generalizes work of Givental for SL n / B in a uniform way to arbitrary type, and can be interpreted as a kind of mirror theorem for the full flag variety G / B . We also prove the existence of a totally positive and totally negative critical point of the ‘superpotential’ in every mirror fiber. Content Type Journal Article Pages 1-27 DOI 10.1007/s00220-011-1308-8 Authors Konstanze Rietsch, Department of Mathematics, King’s College London, Strand, London, UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos Mag A 66(5):697–715, 1992 ), is defined by the following functional: ( E )( u ) = 2 p b | | u (0,·) | | 2 [( H )\dot] 1/2 ([0, h ]) + ó õ L 0   dx ó õ h 0   dy   æ è | u x | 2 + \frac e 2 | u yy | ö ø , where u :[0, L ]×[0, h ] ® \mathbb R is periodic in y and u y = ± 1 almost everywhere. Conti (Cont Mech Therm 17(6):469–476, 2006 ) proved that if b 〉~ e L / h 2 and ( e / L ) 1/3 〈~ h / L , then the minimal specific energy scales like ~ min {( e b / L ) 1/2 , ( e / L ) 2/3 } , as ( e / L ) ® 0 . In the regime ( e b / L ) 1/2 〈〈 ( e / L ) 2/3 , we improve Conti’s results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions. Content Type Journal Article Pages 1-27 DOI 10.1007/s00220-011-1374-y Authors Alessandro Giuliani, Dipartimento di Matematica di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Roma, Italy Stefan Müller, Hausdorff Center for Mathematics & Institute for Applied Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: A standard and a high manganese (Mn) level (10 and 160 μM) were combined with a standard and a high zinc (Zn) level (4 and 64 μM) in the nutrient solution supplied to cucumber in closed-cycle hydroponic units to compensate for nutrient uptake. The concentrations of all nutrients except Mn and Zn were identical in all treatments. The objectives of the experiment were to establish critical Zn and Mn levels in both nutrient solutions and leaves of cucumber grown hydroponically, to assess the impact of gradual Zn and/or Mn accumulation in the external solution on nutrient uptake and gas exchange, and to find whether Mn and Zn have additive effects when the levels of both ions are excessively high in the root zone. The first symptoms of Mn and Zn toxicity appeared when the concentrations of Mn and Zn in the leaves of cucumber reached 900 and 450 mg kg –1 in the dry weight, respectively. Excessively high Mn or/and Zn concentrations in the leaves reduced the fruit biomass production due to decreases in the number of fruits per plant, as well as the net assimilation rate, stomatal conductance, and transpiration rate, but increased the intercellular CO 2 levels. Initially, the Mn or Zn concentrations in the recirculating nutrient solution increased rapidly but gradually stabilized to maximal levels, while the corresponding concentrations in the leaves constantly increased until the end of the experiment. The uptake of Mg, Ca, Fe, and Cu was negatively affected, while that of K and P remained unaffected by the external Mn and Zn levels. The combination of high Mn and Zn seems to have no additive effects on the parameters investigated.

Description: A pot experiment with wheat plants was carried out to study how late application of nitrogen (N) fertilizer affects the use of pre-anthesis N reserves during the grain-filling period. Increasing doses of N fertilizer were applied (0, 40, and 52 mg N plant –1 ), either in two amendments (growth stages GS20 and GS30, according to Zadoks scale) or in three amendments (GS20, GS30, and GS37). The experiment was arranged in a complete randomized three-block design with 129 plants per treatment. The plants were watered daily, harvested every 2 d between anthesis and maturity, and were separated into roots, leaf sheaths, leaf blades, and ears for further N determination. Grain N concentration improved due to a late N application in GS37 by 14% (higher N dose) and by 7% (further splitting the same N-fertilizer dose, respectively). The higher the N-fertilizer dose applied, the greater was the amount of pre-anthesis reserves in vegetative organs, these reserves became later available for remobilization. Although splitting the same N dose in three amendments did not increase the N reserves, these reserves were more efficiently remobilized allowing an improvement in grain N concentration. The fertilizer management did not change the temporary pattern of N accumulation in the ear, but did induce a change in the amount of N remobilized and in the contribution of each organ (root, leaf sheath, leaf blade) to this remobilization. Late N amendment allowed a greater N availability of leaf blades and ear N reserves (from 20% up to 26% and from 19% up to 22%, respectively) for remobilization towards the grain, decreasing the root contribution from 28% down to 15%, while the contribution of leaf sheaths was maintained around 35% irrespective of the N applied.

Description: Flooded rice ( Oryza sativa L.) may contain high arsenic (As) concentrations compared to other grain crops. For the development of measures to reduce the As concentration of rice grains, knowledge about the mobility of As within the rice plant is required. Therefore, to investigate the mobilization of As within the plant, rice was grown in nutrient solution and exposed to As either before flowering, after flowering, or continuously until maturity. Furthermore, rice was grown in four soils under greenhouse and field conditions and the time course of As accumulation in grains during the grain-filling period was investigated. When grown in nutrient solution, As removal at flowering did not reduce As concentrations in polished rice compared to plants supplied with As continuously or after flowering. Plants that received As only after flowering had the same As concentrations in shoot and bran as plants receiving As only before flowering. However, continuous As supply resulted in doubling of As concentrations in both plant parts. In contrast to grain and shoot, the As concentration in the root decreased after As removal compared to the treatments receiving As only after flowering or continuously. The observations indicate that As was mobilized from root or shoot to the grain and that it was accumulated in the grain, although it was not available in nutrient solution during the grain-filling period. In soil experiments, the 1000-grain weight increased up to 2 weeks before harvest in the field as well as in the greenhouse. The As concentration in rice grain was constant during the whole grain-filling period. It was at a similar level under field and greenhouse conditions, and its variation among soils was in the same order indicating that soil was the decisive factor for As concentration in grains. Our results suggest that temporary cultural measures during the cultivation period, for example drainage, might be ineffective because of the mobilization capacity within the rice plant. Moreover, harvest before final maturity of grains would not reduce the As concentration since it remained constant during the grain-filling period.

Description: Recent studies indicate that soil soluble organic nitrogen (SON) plays an important regulatory role in the soil–plant N cycle. The aims of this study were to identify the vertical distribution of SON and its correlation with N mineralization, nitrification, and amidohydrolase activities, in a soil repeatedly amended with cow manure or chemical fertilizer. For this purpose, soil samples were collected from 0–20, 20–40, 40–60, 60–80, and 80–100 cm depths of a calcareous soil, which has been annually amended for 5 y with cow manure (CM) at two rates of 50 (CM 50 ) and 100 (CM 100 ) Mg CM ha –1 y –1 . Treatments with chemical fertilizer (CF) and a control (CT) were also included. Soluble organic N, N mineralization, nitrification rates, as well as L-glutaminase and L-asparaginase activities were determined. Both CM 50 and CM 100 enhanced SON content throughout the soil profile. Nitrogen-mineralization rate (N m ) was increased at the 0–20 cm depth of the CM 100 treatment and remained unaffected at the deeper depths. Nitrification rate (N n ) was significantly higher at the 0–60 cm depth of CM 100 compared to CF and CT. L-glutaminase and L-asparaginase activities were significantly increased at the 0–40 cm depth in both CM 50 and CM 100 compared to CF and CT. The amidohydrolase activities could not be detected below 40 cm, regardless of the fertilizer treatments. Our results suggest that SON makes a minor contribution to N mineralization in deep soil layers. It was also concluded that changes in the SON throughout the soil profile were not associated with changes in the N-transformation rates (N m and N n ) and amidohydrolase activities. While we conclude that SON is a major N pool in the whole profile of the manure applied soil further investigation is required to characterize SON and to investigate the bioavailability of SON for microbial activity in different soil depths.

Description:    In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the family of new Lax-Oleinik type operators with an arbitrary u Î C ( M , \mathbb R 1 ) as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the family of new Lax-Oleinik type operators with an arbitrary u Î C ( M , \mathbb R 1 ) as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case. Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-011-1375-x Authors Kaizhi Wang, School of Mathematics, Jilin University, Changchun, 130012 China Jun Yan, School of Mathematical Sciences, Fudan University, Shanghai, 200433 China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Due to energy crises and stricter environmental regulations, renewable energy sources like bio-methane produced by anaerobic digestion (biogas) become increasingly important. However, the application of slurries produced by biogas fermentation to agricultural land and subsequent ammonia emission may also create environmental risks to the atmosphere and to N-limited ecosystems. Evaluating ammonia loss from agricultural land by model simulation is an important tool of agricultural-systems analysis. The objective of this study was the systematical comparison of ammonia volatilization after application of two types of biogas slurries containing high amounts of energy crops in comparison with conventional animal slurries and to investigate the relative importance of factors affecting the emission process through an empirical model. A high number of ammonia-loss field measurements were carried out in the years 2007/08 in biogas cropping systems in N Germany. The study consisted of simultaneous measurement of NH 3 losses from animal and biogas slurries in multiple-plot field experiments with different N-fertilization levels. The derived empirical model for the calculation of NH 3 losses based on explanatory variables gave good predictions of ammonia emission for both biogas and pig slurries. The root mean square error ( RMSE ) and mean bias error ( MBE ) of the empirical model for validation data were 2.19 kg N ha –1 ( rRMSE 29%) and –1.19 kg N ha –1 , respectively. Biogas slurries produced highest NH 3 emissions compared to the two animal slurries. In view of the explanatory variables included in the model, total NH application rate, slurry type, temperature, precipitation, crop type, and leaf-area index were important for ammonia-volatilization losses.

Description:    In this paper, we deal with global weak solutions of a non-conservative viscous compressible two-phase model in one space dimension. This work extends in some sense the previous work, [Bresch et al., Arch Rat Mech Anal 196:599–629, 2010 ], which provides the global existence of weak solutions in the multi-dimensional framework with 1 〈 γ ± 〈 6 assuming non-zero surface tension. In our study, we strongly improve the results by taking advantage of the one space dimension. More precisely, we obtain global existence of weak solutions without using capillarity terms and for pressure laws with the same range of coefficients as the degenerate barotropic mono-fluid system, namely γ ± 〉 1. Then we prove that any possible vacuum state has to vanish within finite time after which densities are always away from vacuum. This allows to prove that at least one phase corresponding to the global weak solution is a locally in time and space (in a sense to be defined) strong solution after the vacuum states vanish. Our paper may be understood as a non-straightforward generalization to the two-phase flow system of a previous paper [Li et al., Commun Math Phys 281(2):401–444, 2008 ], which treated the usual compressible barotropic Navier-Stokes equations for mono-fluid with a degenerate viscosity. Various important mathematical difficulties occur when we want to generalize those results to the two-phase flows system since the corresponding model is non-conservative. Far from vacuum, it involves a strong coupling between a nonlinear algebraic system and a degenerate PDE system under constraint linked to fractions. Moreover, fractional densities may vanish if densities or fractions vanish: A difficulty is to find estimates on the densities from estimates on fractional densities using the algebraic system. Original approximate systems have also to be introduced compared to the works on the degenerate barotropic mono-fluid system. Note that even if our result concerns “only” the one-dimensional case, it points out possible global weak solutions (for such a non-conservative system) candidates to approach for instance shock structures and to define an appropriate a priori family of paths in the phase space (in numerical schemes) at the zero dissipation limit. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-011-1379-6 Authors Didier Bresch, Laboratoire de Mathématiques, Université of Savoie, Le Bourget Du Lac, 73376 France Xiangdi Huang, Laboratoire de Mathématiques, Université of Savoie, Le Bourget Du Lac, 73376 France Jing Li, Laboratoire de Mathématiques, Université of Savoie, Le Bourget Du Lac, 73376 France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Soil sulfur (S) partitioning among the various pools and changes in tropical pasture ecosystems remain poorly understood. Our study aimed to investigate the dynamics and distribution of soil S fractions in an 8-year-old signal grass ( Brachiaria decumbens Stapf.) pasture fertilized with nitrogen (N) and S. A factorial combination of two N rates (0 and 600 kg N ha –1 y –1 , as NH 4 NO 3 ) and two S rates (0 and 60 kg S ha –1 y –1 , as gypsum) were applied to signal grass pastures during 2 y. Cattle grazing was controlled during the experimental period. Organic S was the major S pool found in the tropical pasture soil, and represented 97% to 99% of total S content. Among the organic S fractions, residual S was the most abundant (42% to 67% of total S), followed by ester-bonded S (19% to 42%), and C-bonded S (11% to 19%). Plant-available inorganic SO 4 -S concentrations were very low, even for the treatments receiving S fertilizers. Low inorganic SO 4 -S stocks suggest that S losses may play a major role in S dynamics of sandy tropical soils. Nitrogen and S additions affected forage yield, S plant uptake, and organic S fractions in the soil. Among the various soil fractions, residual S showed the greatest changes in response to N and S fertilization. Soil organic S increased in plots fertilized with S following the residual S fraction increment (16.6% to 34.8%). Soils cultivated without N and S fertilization showed a decrease in all soil organic S fractions.

Description: A greenhouse pot experiment was carried out to investigate the effects of different P-fertilizer application forms (triple superphosphate [TSP], compost + TSP, TSP-enriched compost) on the growth of ryegrass and the soil microbial biomass. The fertilizers were applied at equivalent doses for all nutrients to a neutral Luvisol in comparison with an acidic Ferralsol. Fertilizer application led to significantly increased contents of microbial biomass C, N, and P. Furthermore, yields of shoot C and root C, and concentrations of P, Ca, Mg, K, Fe, and Mn in shoots and roots were significantly increased. These increases always followed the order TSP 〈 compost + TSP 〈 TSP-enriched compost. Sole TSP application led only to maximum concentrations of N and S. In the Ferralsol, TSP had only minimal positive effect on the P concentration of the grass shoots. The positive effect of TSP-enriched compost, i.e., incubating TSP together with compost for 24 h, did not differ between the neutral Luvisol and the acidic Ferralsol, i.e., the effect is independent of the soil type. Consequently, soluble inorganic P fertilizer should generally be mixed into an organic fertilizer before application to soil.

Description: The physical properties of a Luvisol derived from loess near Bonn, Germany, under different long-term fertilization treatments were examined. For the investigation of the impact of farmyard manure (FYM) on soil strength at the mesoscale (100 to 300 cm 3 soil cores), undisturbed samples were taken from two different depths (10 and 40 cm), either with no fertilization at all, with full mineral fertilization, with FYM only, and with both mineral and organic fertilization. We investigated hydraulic and mechanical parameters, namely precompression stress, pore-size distribution, saturated hydraulic and air conductivity, and calculated pore connectivity. Long-term organic fertilization resulted in significantly more and coarser pores which in addition were more conductant and mechanically stronger by trend. Mineral fertilization also increased pore volume by trend but not pore functionality. Mechanical strength generally increased with fertilization by trend, however, was reduced again when organic and mineral fertilization were combined. Nonetheless, FYM led to relatively higher soil strength as the FYM-treated plots with lower bulk density attained similar soil strength as the unfertilized but denser plots and thus supported the soil-improving impact of organic amendments. The subsoil physical properties were rather unaffected by fertilization, but were dominated by texture.

Description: Little is known about nutrient fluxes and nutrient-use efficiencies in urban and peri-urban agriculture (UPA) of rapidly expanding cities in developing countries. Therefore, horizontal flows of carbon (C), nitrogen (N), phosphorus (P), and potassium (K) as well as leaching losses of mineral N and P were measured over 2 years in three representative agricultural production systems of Kabul. These comprised 21 gardens and 18 fields dedicated to vegetable farming, cereal farming, and table-grape production (vineyards). Across sites (fields and gardens) biennial inputs averaged 375 kg N ha –1 , 155 kg P ha –1 , 145 kg K ha –1 , and 15 kg C ha –1 while with harvests 305 kg N ha –1 , 40 kg P ha –1 , 330 kg K ha –1 , and 7 kg C ha –1 were removed. In vegetable gardens, biennial net balances were 80 kg N ha –1 , 75 kg P ha –1 , –205 kg K ha –1 , and 4 kg C ha –1 , whereas in cereal farming biennial horizontal balances amounted to –155 kg N ha –1 , 20 kg P ha –1 , –355 kg K ha –1 , and 5 kg C ha –1 . In vineyards, corresponding values were 295 kg N ha –1 , 235 kg P ha –1 , 5 kg K ha –1 , and 3 kg C ha –1 . Annual leaching losses in two selected vegetable gardens varied from 70 to 205 kg N ha –1 and from 5 to 10 kg P ha –1 . Night soil and irrigation water were the major sources among the applied nutrient inputs in all studied farming systems, contributing on average 12% and 25% to total N, 22% and 12% to total P, 41% and 53% to total K, and 79% and 10% to total C, respectively. The results suggest that soils in extensive cereal fields are at risk of N and K depletion and in vegetable gardens of K depletion, while vineyards may be oversupplied with nutrients possibly contributing to groundwater contamination. This merits verification.

Description: Residues from biogas production contain essential plant nutrients such as nitrogen (N), phosphorus (P), and potassium (K) but also organic matter, and should be recycled in crop production. For efficient re-use as fertilizers, the availability of nutrients for crops and the effect of the residues on soil fertility need to be evaluated. Focusing on the element P, we compared effects of codigested slurry with dairy slurry, highly soluble mineral NPK fertilizer, and a control without any P supply (NK). Codigested slurry used in this experiment was based on anaerobic digestion of dairy slurry, maize silage, and wheat grain. The fertilizing effects were tested in an 8-week pot experiment on a sandy and a loamy soil using two crop species ( Zea mays L., Amaranthus cruentus L.). The plant P uptake was up to 64% greater in the slurry treatments than in the treatment without P. The effect of codigested slurry on P uptake was comparable to that of dairy slurry and mineral P. Plant N uptake from codigested slurry was lower than that from mineral N (NK, NPK), but tended to be higher than from dairy slurry. The water-soluble and double lactate–soluble P content of the soil was lower in the slurry treatments than in the mineral-P treatments and accompanied by higher contents of microbial-bound P. Differences between both organic fertilizers were detected for dehydrogenase activity which was up to 32% lower in soils fertilized with codigested slurry than it was in soils fertilized with dairy slurry. Our results indicate that codigestion of slurries in biogas plants does not substantially alter their fertilizer value as P and N sources for crops.

Description: The effect of different deficit-irrigation treatments on the dynamics of mineral nutrients in leaves of peach trees growing under Mediterranean conditions was studied. Treatments consisted of a control, continuous deficit irrigation, regulated deficit irrigation, and partial root drying. The dynamics of nutrients were unchanged by the water deficits, though the amount absorbed was slightly modified. The advantages of deficit-irrigation strategies with regard to water-use efficiency were accompanied by the absence of any harmful effect on leaf mineral nutrition.

Description: It has been suggested that short-term field experiments are not suitable for the quantitative assessment of cropping-systems impact on soil organic matter (SOM) levels in arable soils, as expectable temporal changes are very small compared to a large spatial variation of SOM background levels. However, applying an optimized sampling design based on repeated sampling in small plots, we were able to detect soil total carbon (STC) and nitrogen (STN) changes in the magnitude of ≈ 1% (STC) and ≈ 2% (STN) of background levels with only four replications, respectively. Gradually enlarging the sample size up to n = 24 did not considerably improve change detectability with STC, but with STN ( n = 15 allowing for the dection of ≈ 1% change of background levels). The common calculation of minimum detectable differences (MDD) based on a state analysis of SOM levels instead of repeated measurements considerably underestimated change detectability.

Description: Two experiments were conducted to study the effect of grafting on nitrogen-use efficiency (NUE) in mini-watermelon plants. In the first study, mini-watermelon plants ( Citrullus lanatus [Thumb.] Matsum. and Nakai cv. Minirossa) either ungrafted or grafted onto Macis, Vita ( Lagenaria siceraria [Mol.] Standl.), PS1313, and RP15 ( Cucurbita maxima Duchesne × Cucurbita moschata Duchesne) rootstocks grown in hydroponics were compared in terms of shoot dry biomass, leaf area, root-to-shoot ratio, SPAD index, shoot N uptake, and nitrate reductase (NR) activity 40 d after transplantation in response to nitrate concentration in the nutrient solution (0.5, 2.5, 5, 10, 15, or 20 mM of NO ). In the second experiment, the suitability of a selected rootstock with high NUE (Vita) to improve crop performance and NUE of grafted mini-watermelon plants was evaluated under field conditions. In the hydroponic experiment mini-watermelon grafted onto Vita rootstock needed the lowest nitrate concentration (1.31 mM of NO 3 ) in the nutrient solution to reach half maximum shoot dry weight. Total leaf area, SPAD index, and shoot N uptake increased in response to an increase of N concentration in the nutrient solution. At 2.5 mM NO , mini-watermelon grafted on either Vita or RP15 had the highest NR activity whereas no significant difference was observed at 10 mM NO . The open-field study indicated that increasing N-fertilization rates from 0 to 100 kg ha –1 improved total and marketable yields of mini-watermelon plants while decreasing NUE. When averaged over N levels, the marketable yield, NUE, N-uptake efficiency, and N-utilization efficiency were significantly higher by 39%, 38%, 21%, and 17%, respectively, in Minirossa grafted onto Vita compared to ungrafted Minirossa plants. Therefore, grafting mini-watermelon plants onto selected rootstocks can be used as a quick and effective method for improving productivity and NUE.

Description:    Brolin-Lyubich measure λ R of a rational endomorphism R : ^ \mathbb C   ® ^ \mathbb C   with deg R  ≥ 2 is the unique invariant measure of maximal entropy h l R = h top ( R )=log d . Its support is the Julia set J ( R ). We demonstrate that λ R is always computable by an algorithm which has access to coefficients of R , even when J ( R ) is not computable. In the case when R is a polynomial, the Brolin-Lyubich measure coincides with the harmonic measure of the basin of infinity. We find a sufficient condition for computability of the harmonic measure of a domain, which holds for the basin of infinity of a polynomial mapping, and show that computability may fail for a general domain. Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-011-1363-1 Authors Ilia Binder, Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada Mark Braverman, Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada Cristobal Rojas, Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada Michael Yampolsky, Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995 ). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4-volume spanned by five independent events, is shown to be normal. Its spectrum is pure point with a finite distance (of the order of the fourth power of the Planck length) away from the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-011-1358-y Authors D. Bahns, Courant Research Center Mathematics, University of Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany S. Doplicher, Dipartimento di Matematica, Università degli Studi di Roma “Sapienza”, P.le A. Moro 2, 00185 Roma, Italy K. Fredenhagen, II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany G. Piacitelli, SISSA – Via Bonomea 265, 34136 Trieste, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study one–dimensional Ising spin systems with ferromagnetic, long–range interaction decaying as n −2+ α , a Î [0,\frac 12] , in the presence of external random fields. We assume that the random fields are given by a collection of symmetric, independent, identically distributed real random variables, which are gaussian or subgaussian with variance θ . We show that when the temperature and the variance of the randomness are sufficiently small, with overwhelming probability with respect to the random fields, the typical configurations, within intervals centered at the origin whose length grow faster than any power of θ −1 , are intervals of + spins followed by intervals of − spins whose typical length is @   q - \frac2(1 - 2 a ) for 0 ≤ α  〈 1/2 and between e \frac1 q and e \frac 1 q 2 for α  = 1/2. Content Type Journal Article Pages 1-25 DOI 10.1007/s00220-011-1371-1 Authors Marzio Cassandro, Dipartimento di Fisica, Universitá di Roma “La Sapienza”, P.le A. Moro, 00185 Roma, Italy Enza Orlandi, Dipartimento di Matematica, Universitá di Roma Tre, L.go S.Murialdo 1, 00146 Roma, Italy Pierre Picco, LATP, CMI, UMR 6632, CNRS, Université de Provence, 39 rue Frederic Joliot Curie, 13453 Marseille Cedex 13, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a large lattice system of unbounded continuous spins that are governed by a Ginzburg-Landau type potential and a weak quadratic interaction. We derive the logarithmic Sobolev inequality (LSI) for Kawasaki dynamics uniform in the boundary data. The scaling of the LSI constant is optimal in the system size and our argument is independent of the geometric structure of the system. The proof consists of an application of the two-scale approach of Grunewald, Otto, Westdickenberg & Villani. Several ideas are needed to solve new technical difficulties due to the interaction. Let us mention the application of a new covariance estimate, a conditioning technique, and a generalization of the local Cramér theorem. Content Type Journal Article Pages 1-44 DOI 10.1007/s00220-011-1326-6 Authors Georg Menz, Max Planck Institute for Mathematics in the Sciences, Inselstr. 22 - 26, Leipzig, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We show that for all q in the interval (−1, 1), the Fock representation of the q -commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C *-algebra generated by the Fock representation of the q -commutation relations is exact. An immediate consequence is that the q -Gaussian von Neumann algebra is weakly exact for all q in the interval (−1, 1). Content Type Journal Article Pages 1-18 DOI 10.1007/s00220-011-1323-9 Authors Matthew Kennedy, Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Alexandru Nica, Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-011-1312-z Authors Jacques Franchi, IRMA, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France Yves Le Jan, Université Paris Sud 11, Mathématiques, Bâtiment 425, 91405 Orsay, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider the nonlinear Schrödinger equation ( - D + V ( x )) u = G ( x ) | u | p - 1 u ,     x Î \mathbb R n with V ( x ) = V 1 ( x ), Γ( x ) = Γ 1 ( x ) for x 1  〉 0 and V ( x ) = V 2 ( x ), Γ( x ) = Γ 2 ( x ) for x 1  〈 0, where V 1 , V 2 , Γ 1 , Γ 2 are periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state H 1 solutions (surface gap soliton ground states) for 0 〈 min σ (−Δ +  V ). Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with V ≡ V 1 , Γ ≡ Γ 1 and V ≡ V 2 , Γ ≡ Γ 2 ) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators - \tfrac d 2 dx 2 + V 1 ( x ) and - \tfrac d 2 dx 2 + V 2 ( x ) . Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-011-1320-z Authors Tomáš Dohnal, Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany Michael Plum, Institut für Analysis, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany Wolfgang Reichel, Institut für Analysis, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The quantum double of the Haagerup subfactor, the first irreducible finite depth subfactor with index above 4, is the most obvious candidate for exotic modular data. We show that its modular data D Hg fits into a family D w Hg 2 n +1 , where n ≥  0 and w Î \mathbb Z 2 n +1 . We show D 0 Hg 2 n +1 is related to the subfactors Izumi hypothetically associates to the cyclic groups \mathbb Z 2 n +1 . Their modular data comes equipped with canonical and dual canonical modular invariants; we compute the corresponding alpha-inductions, etc. In addition, we show there are (respectively) 1, 2, 0 subfactors of Izumi type \mathbb Z 7 , \mathbb Z 9 and \mathbb Z 3 2 , and find numerical evidence for 2, 1, 1, 1, 2 subfactors of Izumi type \mathbb Z 11 ,\mathbb Z 13 ,\mathbb Z 15 ,\mathbb Z 17 ,\mathbb Z 19 (previously, Izumi had shown uniqueness for \mathbb Z 3 and \mathbb Z 5 ), and we identify their modular data. We explain how D Hg (more generally D w Hg 2 n +1 ) is a graft of the quantum double D Sym (3) (resp. the twisted double D w D 2 n +1 ) by affine so(13) (resp. so (4 n 2 +4 n +5) ) at level 2. We discuss the vertex operator algebra (or conformal field theory) realisation of the modular data D w Hg 2 n +1 . For example we show there are exactly 2 possible character vectors (giving graded dimensions of all modules) for the Haagerup VOA at central charge c = 8. It seems unlikely that any of this twisted Haagerup-Izumi modular data can be regarded as exotic, in any reasonable sense. Content Type Journal Article Pages 1-50 DOI 10.1007/s00220-011-1329-3 Authors David E. Evans, School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG Wales, UK Terry Gannon, Department of Mathematics, University of Alberta, Edmonton, AB T6G 2G1, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂ x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with periodic boundary conditions, so KAM tori and thus quasi-periodic solutions are obtained for them. Content Type Journal Article Pages 1-45 DOI 10.1007/s00220-011-1353-3 Authors Jianjun Liu, School of Mathematical Sciences and Key Lab of Math. for Nonlinear Science, Fudan University, Shanghai, 200433 P.R. China Xiaoping Yuan, School of Mathematical Sciences and Key Lab of Math. for Nonlinear Science, Fudan University, Shanghai, 200433 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B and B - \frac12,\frac12 4 (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that ( ANS ν ) has a unique global solution with initial data u 0 = ( u 0 h , u 0 3 ) which satisfies || u 0 h || B exp æ è \frac C n 4 || u 0 3 || B 4 ö ø £ c 0 n or || u 0 h || B - \frac12,\frac12 4 exp æ è \frac C n 4 || u 0 3 || B - \frac12,\frac12 4 4 ö ø £ c 0 n for some c 0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, ~ L p t   ( B ) , we introduced here sort of weighted Chemin-Lerner type spaces, ~ L 2 t , f   ( B ) for some apropriate L 1 function f ( t ). Content Type Journal Article Pages 1-47 DOI 10.1007/s00220-011-1350-6 Authors Marius Paicu, Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence Cedex, France Ping Zhang, Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190 China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski (Hyperbolic Equ. 4(3):401–433, 2007 ) to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization of (Hyperbolic Equ. 4(3):401–433, 2007 ) is a key component for extending Klainerman and Rodnianski’s breakdown criterion result for Einstein-vacuum spacetimes in (J. Amer. Math. Soc. 23(2):345–382, 2009 ) to Einstein-Maxwell and Einstein-Yang-Mills spacetimes. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-011-1273-2 Authors Arick Shao, Department of Mathematics, Princeton University, Princeton, NJ 08544, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a family of time-dependent dephasing Lindblad generators which model the monitoring of the instantaneous Hamiltonian of a system by a Markovian bath. In this family the time dependence of the dephasing operators is (essentially) governed by the instantaneous Hamiltonian. The evolution in the adiabatic limit admits a geometric interpretation and can be solved by quadrature. As an application we derive an analog of the Landau-Zener tunneling formula for this family. Content Type Journal Article Pages 1-7 DOI 10.1007/s00220-011-1269-y Authors J. E. Avron, Department of Physics, Technion, 32000 Haifa, Israel M. Fraas, Department of Physics, Technion, 32000 Haifa, Israel G. M. Graf, Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland P. Grech, Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In n -dimensional Euclidean space let us be given an infinitely differentiable real valued function V that is bounded below. We associate with the formal operator that sends a complex valued function ψ into −div(grad ψ ) +  V ψ a uniquely defined self adjoint operator which we will denote by −Δ +  V . If ψ 0 is any eigenfunction of the self adjoint operator −Δ +  V we prove that a necessary and sufficient condition for ψ 0 to never equal zero is that the eigenspace to which ψ 0 belongs contain a positive function. In this case the eigenspace must be one dimensional. The same result holds on any complete connected Riemannian manifold whose first Betti number is zero. Content Type Journal Article Pages 1-5 DOI 10.1007/s00220-011-1272-3 Authors Sol Schwartzman, Math. Department, University of Rhode Island, Kingston, RI 02881, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature. All the rigorous approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the infinitesimal version of the former). We present an approach based on polymer expansions of statistical mechanics. Despite the fact that our approach is elementary, our results are slightly sharper than those contained in the literature up to now. We show that, whenever the small quantum system is known to admit a Markov approximation (Pauli master equation aka Lindblad equation) in the weak coupling limit, and the Markov approximation is exponentially mixing, then the weakly coupled system approaches a unique invariant state that is perturbatively close to its Markov approximation. Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-011-1247-4 Authors W. De Roeck, Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany A. Kupiainen, Department of Mathematics, University of Helsinki, P. O. Box 68, Helsinki, FIN-00014 Finland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: An evaluation of the factors determining the occurrence and the properties of soils with low permeability occurring in vast areas in S Portugal was carried out taking into account the terrain morphology and the geology of the region. This paper deals with the variation patterns of the physical and chemical characteristics of soils from several soil toposequences that occur under different gradient slopes and on different parent rocks. Spatial variation of soil properties mainly depends on the composition of their cation-exchange complex, as the role of other factors, such as the mineralogy of the clay fraction, were of minor importance. There is often a stronger increment of Na and/or Mg than of Ca with depth, causing a variable degree of sodicity in some of these soils, to which waterlogging tendency of their upper horizons is related. Though the occurrence of these features is determined by the nature of the parent rock, their degree of expression varies primarily according to the topographic position of soils. Therefore, a catenary distribution including nonsodic Cambisols or Luvisols in the hillcrests and Stagnic Solonetz or Sodic Luvisols or Sodic Stagnosols in the topographic lows is common. Such soil characteristics are of utmost importance for irrigation suitability and management of these soils, and for environmental impacts assessment, as the region is vulnerable to desertification.

Description: Oxisols cover ≈ 23% of the land surface in the tropics and are utilized extensively for agricultural purposes in the tropical countries. Under the variable input types of agricultural systems practiced locally, some of these soils still appear to have problems in terms of proper soil classification and subsequently hinder attempts to implement sustainable agro-management protocols. The definition for Oxisols in Soil Survey Staff (1999) indicates that additional input is still required to refine the definition in order to resolve some of the outstanding classification problems. Therefore, the objective of this study is to examine the properties of some Oxisols and closely related soils in order to evaluate the classification of these soils. Soils from Brazil, several countries in Africa, and Malaysia were used in this study. Field observations provided the first indication that some of the presently classified kandi-Alfisols and kandi-Ultisols were closer to Oxisols in terms of their properties. Water-retention differences and apparent CEC of the subsurface horizons also supported this idea. The types of extractable Fe oxides and external specific surface areas of the clay fractions showed that many kandic horizons have surface properties that are similar to the oxic horizons. Micromorphology indicated that the genetic transition from the argillic to the oxic involves a diminishing expression of the argillic. Properties, such as CEC, become dominant. The kandic horizon is therefore inferred as a transition to the oxic horizon. It is proposed that the Oxisols be keyed out based only on the presence of an oxic horizon and an iso–soil temperature regime. The presence of a kandic horizon will be reflected at lower levels in Oxisols. The Oxisols will now be exclusive to the intertropical belt with an iso–soil temperature regime. The geographic extend of the Oxisols would increase and that of kandi-Alfisols and Ultisols would decrease. A few kandi-Alfisols and Ultisols in the intertropical area will have low CEC which would fail the weatherable mineral contents. The kandic subgroups of some Alfisols and Ultisols will be transitional between the low (〈 16 cmol c [kg clay] –1 )- and high (〉 24 cmol c [kg clay] –1 )-activity clay soils. The proposed changes to classification will contribute to a better differentiation of the landscape units in the field. Testing of the proposed classification on some Malaysian soils showed that the new definition for Oxisols provides a better basis for the classification of the local soils and the development of meaningful soil-management groups for plantations.

Description: Variability in soil properties is a complication for fertilization, irrigation, and amendment application. However, only limited progress has been made in managing soil variability for uniform productivity and increased water-use efficiency. This study was designed to ameliorate the poor-productivity areas of the variable sandy soils in Florida citrus groves by using frequent small irrigations and applying organic and inorganic soil amendments. Two greenhouse experiments were set up with sorghum and radish as bioassay crops in a randomized complete block design (RCBD). The factors studied were two soil-productivity classes (very poor and very good), two water contents (50% and 100% of field capacity), two amendments (phosphatic clay and Fe humate), and two amendment rates (10 and 25 g kg –1 for sorghum and 50 and 100 g kg –1 for radish). Amendments applied at 50 and 100 g kg –1 increased the water-holding capacity (WHC) of poor soil by 2- to 6-fold, respectively. The lower rates (10 and 25 g kg –1 ) of amendments were not effective in enhancing sorghum growth. The higher rates (50 and 100 g kg –1 ) doubled the radish growth as compared to the control. The results indicate that rates greater than 50 g kg –1 of both amendments were effective in improving water retention and increasing productivity. Irrigation treatment of 100% of field capacity (FC) increased the sorghum and radish growth by about 2-fold as compared with the 50%–water content treatment. The results suggest that the root-zone water content should be maintained near FC by frequent small irrigations to enhance water availability in excessively drained sandy soils. In addition, application of soil amendments in the root zone can enhance the water retention of these soils. Furthermore, managing variable sandy soils with WHC-based irrigation can increase water uptake and crop production in the poor areas of the grove.

Description:    In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method based on evaluating the primitive invariants of Chevalley on the Lax operators with spectral parameter. As part of our analysis, we will develop several results concerning the algebra of invariant polynomials on simple Lie algebras and their expansions. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-011-1359-x Authors Luen-Chau Li, Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA Zhaohu Nie, Department of Mathematics, Pennsylvania State University, Altoona Campus, 3000 Ivyside Park, Altoona, PA 16601, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We develop a theory of f -coordinated (quasi-) modules for a general nonlocal vertex algebra where f is what we call an associate of the one-dimensional additive formal group. By specializing f to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica (New Series) 11:349–397, 2005 ). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum vertex algebras and f -coordinated modules to a certain quantum βγ -system explicitly. Content Type Journal Article Pages 1-39 DOI 10.1007/s00220-011-1364-0 Authors Haisheng Li, Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009 ; Commun Math Phys 288(3):919–942, 2009 ) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009 ; Commun Math Phys 288(3):919–942, 2009 ) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-011-1362-2 Authors PoNing Chen, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Mu-Tao Wang, Department of Mathematics, Columbia University, New York, NY 10027, USA Shing-Tung Yau, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616